Global Polynomial Synchronization of Proportional Delay Memristive Competitive Neural Networks With Uncertain Parameters for Image Encryption

The global polynomial synchronization (GPS) is investigated for memristive competitive neural networks (MCNNs) with proportional delays and uncertain parameters. First, via drawing support from differential inclusion theory and adopting the time-variant state feedback controllers, their error systems are synthesized into a vector form MCNNs. Then, a new proportional delay differential inequality (PDDI) is established through norm definition and Lipschitz condition for the vector form MCNNs mentioned-above. Several algebraic forms of synchronization criteria for the system proposed are achieved by applying the new PDDI. Each of these criteria is represented by only one inequality, rather than in the form of components, which facilitates validation. Compared to the commonly used method for constructing Lyapunov functionals in studying MCNNs, it is more concise. Ultimately, numerical examples are used to inspect the results acquired, and the GPS of one example is applied in image encryption and decryption. The empirical outcomes demonstrat the efficacy of the employed synchronization control approach, exhibiting robust resilience and heighten security in secure communication applications.